Recent Trends in Sliding Mode Control

In control theory, sliding mode control, or SMC, is a nonlinear control method that alters the dynamics of a nonlinear system by application of a discontinuous control signal that forces the system to 'slide' along a cross-section of the system's normal behaviour. This book describes...

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Bibliographic Details
Main Authors Fridman, Leonid, Barbot, Jean-Pierre, Plestan, Franck
Format eBook
LanguageEnglish
Published Stevenage The Institution of Engineering and Technology 2016
Institution of Engineering and Technology (The IET)
Institution of Engineering & Technology
Institution of Engineering and Technology
Edition1
Subjects
Automatic control engineering
Computer Hardware Engineering
Electronics
Networks & Sensors
Sliding mode control
TECHNOLOGY & ENGINEERING
variable structure systems
linear quadratic control
Online AccessGet full text
ISBN9781785610769
1785610767
DOI10.1049/PBCE102E

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Table of Contents:
  • Part 1: Novel sliding mode algorithms -- Chapter 1.1: Lyapunov approach to higher-order sliding mode design -- Chapter 1.2: Sliding surface design for higher-order sliding modes -- Chapter 1.3: Robust output control of systems subjected to perturbations via high-order sliding modes observation and identification -- Chapter 1.4: Construction of Lyapunov functions for high-order sliding modes -- -- Part 2: Properties of sliding mode algorithms -- Chapter 2.1: Homogeneity of differential inclusions -- Chapter 2.2: Minimax observer for sliding mode control design -- Chapter 2.3: -- -- -Gain analysis of sliding mode dynamics -- Chapter 2.4: Analysis of transient motions in variable-structure systems through the dynamic harmonic balance principle -- -- Part 3: Discretization of sliding-mode controllers -- Chapter 3.1: On discretization of high-order sliding modes -- Chapter 3.2: Experimental results on implicit and explicit time-discretization of equivalent control-based sliding mode control -- Chapter 3.3: A generalized reaching law for discrete-time sliding mode -- -- Part 4: Applications -- Chapter 4.1: Conventional and adaptive second-order sliding mode control of a wind energy conversion system -- Chapter 4.2: Sliding mode control of a fuel cell–based electric power system: multiple modular configurations -- Chapter 4.3: Networked model-based event-triggered sliding mode control -- Chapter 4.4: Step-by-step super-twisting observer for DC series motor in the presence of magnetic saturation -- Chapter 4.5: Sliding mode control of LCL full-bridge rectifiers -- Chapter 4.6: Adaptive solutions for robust control of electropneumatic actuators --
  • Title Page Preface Table of Contents 1.1 Lyapunov Approach to Higher-Order Sliding Mode Design 1.2 Sliding Surface Design for Higher-Order Sliding Modes 1.3 Robust Output Control of Systems Subjected to Perturbations via High-Order Sliding Modes Observation and Identification 1.4 Construction of Lyapunov Functions for High-Order Sliding Modes 2.1 Homogeneity of Differential Inclusions 2.2 Minimax Observer for Sliding Mode Control Design 2.3 2-Gain Analysis of Sliding Mode Dynamics 2.4 Analysis of Transient Motions in Variable-Structure Systems through the Dynamic Harmonic Balance Principle 3.1 On Discretization of High-Order Sliding Modes 3.2 Experimental Results on Implicit and Explicit Time-Discretization of Equivalent Control-Based Sliding Mode Control 3.3 A Generalized Reaching Law for Discrete-Time Sliding Mode 4.1 Conventional and Adaptive Second-Order Sliding Mode Control of a Wind Energy Conversion System 4.2 Sliding Mode Control of a Fuel Cell-Based Electric Power System: Multiple Modular Configurations 4.3 Networked Model-Based Event-Triggered Sliding Mode Control 4.4 Step-by-Step Super-Twisting Observer for DC Series Motor in the Presence of Magnetic Saturation 4.5 Sliding Mode Control of LCL Full-Bridge Rectifiers 4.6 Adaptive Solutions for Robust Control of Electropneumatic Actuators Index
  • 2.2 - Minimax observer for sliding mode control design -- Abstract -- 2.2.1 - Introduction -- 2.2.2 - Notation -- 2.2.3 - Problem statement -- 2.2.4 - Min-max optimal state observer design -- 2.2.5 - Control design -- 2.2.6 - Numerical simulations -- 2.2.7 - Conclusion -- References -- 2.3 - L2-Gain analysis of sliding mode dynamics -- Abstract -- 2.3.1 - Introduction -- 2.3.2 - Generic L2-gain analysis -- 2.3.3 - A case study: first order SM dynamics -- 2.3.4 - A case study: second order SM dynamics -- References -- 2.4 - Analysis of transient motions in variable-structure systems through the dynamic harmonic balance principle -- Abstract -- 2.4.1 - Introduction -- 2.4.2 - Transient oscillations in Lur'es systems -- 2.4.3 - Motions in the vicinity of a periodic solution -- 2.4.4 - DHB accounting for frequency rate of change (full DHB) -- 2.4.5 - Analysis of transient motions of rocking block through DHB -- 2.4.6 - Analysis of asymptotic second-order SM system using DHB principle -- 2.4.7 - Conclusions -- References -- Section 3 - Discretization of sliding-mode controllers -- 3.1 - On discretization of high-order sliding modes -- Abstract -- 3.1.1 - Introduction -- 3.1.2 - Preliminaries: sliding order and SM accuracy -- 3.1.3 - Accuracy of homogeneous differential inclusions -- 3.1.4 - Homogeneous continuous-time SM control -- 3.1.5 - Discretization of SM differentiators -- 3.1.6 - Discretization of SMs -- 3.1.7 - Conclusions -- References -- 3.2 - Experimental results on implicit and explicit time-discretization of equivalent control-based sliding mode control -- Abstract -- 3.2.1 - Introduction -- 3.2.2 - Dynamics of the plant and controllers -- 3.2.3 - Experimental results -- 3.2.4 - Numerical analysis of the saturation controller -- 3.2.5 - Conclusion -- Appendix 1 - Some basic convex analysis tools -- Acknowledgments -- References
  • Appendix 3 - Proof of theorem 4.3.3 -- Appendix 4 - Proof of theorem 4.3.4 -- References -- 4.4 - Step-by-step super-twisting observer for DC series motor in the presence of magnetic saturation -- Abstract -- 4.4.1 - Introduction -- 4.4.2 - Mathematical model -- 4.4.3 - Observability analysis of the DC series motor -- 4.4.4 - Observer design -- 4.4.5 - Estimator -- 4.4.6 - Observer and estimator discretization -- 4.4.7 - Experimental results -- 4.4.8 - Conclusion -- References -- 4.5 - Sliding mode control of LCL full-bridge rectifiers -- Abstract -- 4.5.1 - Introduction -- 4.5.2 - Modeling LCL rectifiers -- 4.5.3 - Overall control scheme -- 4.5.4 - Control design of an LCL single-phase rectifier -- 4.5.5 - Control design of an LCL three-phase three-wire rectifier -- 4.5.6 - Control design of an LCL three-phase four-wire rectifier -- 4.5.7 - Conclusions -- References -- 4.6 - Adaptive solutions for robust control of electropneumatic actuators -- Abstract -- 4.6.1 - Introduction -- 4.6.2 - Electropneumatic system -- 4.6.3 - Adaptive twisting controller -- 4.6.4 - Adaptive output feedback controller -- 4.6.5 - Adaptive super-twisting controller -- 4.6.6 - Experimental comparisons -- 4.6.7 - Conclusions -- References -- Index
  • Intro -- Contents -- Preface -- Acknowledgments -- List of contributors -- Section 1 - Novel sliding mode algorithms -- 1.1 - Lyapunov approach to higher-order sliding mode design -- Abstract -- 1.1.1 - Introduction -- 1.1.2 - Basic mathematical tools -- 1.1.3 - The standard HOSMC problem -- 1.1.4 - Homogeneous HOSMC design by using CLFs -- 1.1.5 - Two r-homogeneous CLFs -- 1.1.6 - Differences with the classical families of HOSMCs -- 1.1.7 - Gain tuning -- 1.1.8 - An academic example -- 1.1.9 - Conclusions -- 1.1.10 - Explicit expressions for i−1 -- Acknowledgments -- References -- 1.2 - Sliding surface design for higher-order sliding modes -- Abstract -- 1.2.1 - Introduction -- 1.2.2 - Problem statement -- 1.2.3 - Preliminaries -- 1.2.4 - Pole placement -- 1.2.5 - Singular LQR -- 1.2.6 - Conclusions -- Acknowledgment -- References -- 1.3 Robust output control of systems subjected to perturbations via high-order sliding modes observation and identification -- Abstract -- 1.3.1 - Introduction -- 1.3.2 - Notation -- 1.3.3 - Problem statement -- 1.3.4 - HOSM observer -- 1.3.5 - Control of systems affected by matched perturbations -- 1.3.6 - Control of systems affected by unmatched perturbations -- 1.3.7 - Conclusions -- References -- 1.4 - Construction of Lyapunov functions for high-order sliding modes -- Abstract -- 1.4.1 - Introduction -- 1.4.2 - Trajectory integration method -- 1.4.3 - Variable reduction method -- 1.4.4 - Generalized forms approach -- 1.4.5 - Conclusions -- Acknowledgment -- References -- Section 2 - Properties of sliding mode algorithms -- 2.1 - Homogeneity of differential inclusions -- Abstract -- 2.1.1 - Introduction -- 2.1.2 - Preliminaries -- 2.1.3 - Homogeneous DIs -- 2.1.4 - Qualitative results on homogeneous discontinuous systems -- 2.1.5 - Conclusion -- References
  • 3.3 - A generalized reaching law for discrete-time sliding mode -- Abstract -- 3.3.1 - Introduction -- 3.3.2 - Definition of the bands -- 3.3.3 - Digital application of continuous sliding mode control -- 3.3.4 - Simulation example -- 3.3.5 - The generalized reaching algorithm -- 3.3.6 - Summary -- References -- Section 4 - Applications -- 4.1 - Conventional and adaptive second-order sliding mode control of a wind energy conversion system -- Abstract -- 4.1.1 - Introduction -- 4.1.2 - Wind energy conversion system -- 4.1.3 - Sliding manifold design -- 4.1.4 - Adaptive SOSM design -- 4.1.5 - Simulation results -- 4.1.6 - Conclusions -- A.1 - WECS full-order dynamical model -- A.2 - Nominal values of the parameters -- Acknowledgments -- References -- 4.2 - Sliding mode control of a fuel cell-based electric power system: multiple modular configurations -- Abstract -- 4.2.1 - Introduction -- 4.2.2 - Background of direct output voltage tracking in DC-DC boost converters: nonminimum phase phenomenon -- 4.2.3 - Mathematical model of PEMFC/multiple modular DC-DC boost converter with an individual load configuration of an electric power system -- 4.2.4 - Mathematical model of PEMFC/multiple modular DC-DC boost converter with shared load configuration of an electric power system -- 4.2.5 - Problem formulation -- 4.2.6 - Controller design -- 4.2.7 - Simulation study -- 4.2.8 - Conclusion -- References -- 4.3 - Networked model-based event-triggered sliding mode control -- Abstract -- 4.3.1 - Introduction -- 4.3.2 - Model-based event-triggered control: preliminaries -- 4.3.3 - Strategy 1: model-based event-triggered SMC -- 4.3.4 - Strategy 2: model-based event-triggered SMC with pseudo-equivalent control -- 4.3.5 - Illustrative example -- 4.3.6 - Conclusions -- Appendix 1 - Proof of theorem 4.3.1 -- Appendix 2 - Proof of theorem 4.3.2